$\dfrac{ -5l + 5m }{ 9 } = \dfrac{ 2l + 9n }{ -5 }$ Solve for $l$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -5l + 5m }{ {9} } = \dfrac{ 2l + 9n }{ -5 }$ ${9} \cdot \dfrac{ -5l + 5m }{ {9} } = {9} \cdot \dfrac{ 2l + 9n }{ -5 }$ $-5l + 5m = {9} \cdot \dfrac { 2l + 9n }{ -5 }$ Multiply both sides by the right denominator. $-5l + 5m = 9 \cdot \dfrac{ 2l + 9n }{ -{5} }$ $-{5} \cdot \left( -5l + 5m \right) = -{5} \cdot 9 \cdot \dfrac{ 2l + 9n }{ -{5} }$ $-{5} \cdot \left( -5l + 5m \right) = 9 \cdot \left( 2l + 9n \right)$ Distribute both sides $-{5} \cdot \left( -5l + 5m \right) = {9} \cdot \left( 2l + 9n \right)$ ${25}l - {25}m = {18}l + {81}n$ Combine $l$ terms on the left. ${25l} - 25m = {18l} + 81n$ ${7l} - 25m = 81n$ Move the $m$ term to the right. $7l - {25m} = 81n$ $7l = 81n + {25m}$ Isolate $l$ by dividing both sides by its coefficient. ${7}l = 81n + 25m$ $l = \dfrac{ 81n + 25m }{ {7} }$